Although the thread was originally asking "have you ever lost a card to or from an auction house," I once lost a card while AT an auction house.
I consigned a T207 set over 10 years ago and the auction house lost the Lowdermilk which was in around excellent condition (it was not slabbed). Apparently it was accidentally "thrown away" while being photographed.
When they discovered their loss, they called immediately and they agreed to what I felt was a reasonable and fair price and quickly sent a check to me in that amount. I was ok with it but regretted that the one of the three "key" cards in the set was gone and the set became a near set. Still, I appreciated the way the loss was handled by Bill Mastro.
As far as shippping valuable cards goes, I always use registered mail. I agree with Barry, it is the best.